1. Field of the Invention
The present invention relates to Fourier transform-based phasor estimation, and, more particularly, to a Fourier transform-based phasor estimation method and apparatus capable of eliminating the influence of exponentially decaying DC offsets, which can accurately estimate the phasor of an input signal, including one or more DC offsets, by eliminating the influence of the DC offsets from the input signal.
2. Description of the Related Art
A Discrete Fourier Transform (DFT) is a method generally used to estimate the phasor of an fundamental frequency component in various types of protection and control devices, and enables a phasor to be accurately estimated when conditions, such as i) a condition in which the frequency of a highest-order harmonic, included in an input signal, is lower than ½ of a sampling frequency, and ii) a condition in which a non-periodic signal, for example, an exponentially decaying DC offset component, is not included in the input signal, are satisfied.
In practice, the condition i) can be satisfied by filtering an input signal using a low-pass or band-pass filter, but the condition ii) is not satisfied in the case of fault current including an exponentially decaying DC offset component, other than a sinusoidal component.
Fault current, flowing through a power system when a fault occurs, can be represented by a combination of sinusoidal components and an exponentially decaying DC offset component. When a fault resistor exists, fault current includes two or more DC offset components.
Further, current flowing through a power system is measured by a Current Transformer (CT), and the secondary current of the CT, used as the input of a protection relay, includes another DC offset component due to the influence of the CT circuit.
An exponentially decaying DC offset component is a non-periodic signal, and exhibits characteristics of having arbitrary values in all frequency bands. Accordingly, when a phasor is calculated using a DFT, the DC offset component greatly influences accuracy, which results in the mal-operation/dead operation of a protection relay and the decrease in the accuracy of a measuring device. Therefore, in order to implement a high-performance protection and control device, the DC offset component should be taken in to consideration in calculating the phasor of the fundamental frequency component of a relaying signal.
For reducing or eliminating the influence of a DC offset, a method using a digital mimic filter has been proposed, and this method is configured such that the time constant of a DC offset is assumed to be a specific value at the time of designing a mimic filter.
However, since the time constant of a DC offset component varies depending on the system configuration and fault conditions such as a fault location, a fault resistance, etc., an error occurs when the time constant of a DC offset, included in fault current, differs from the time constant assumed when the filter is designed.
In order to remove the error caused by the difference between the actual and presumed time constants of the DC offset, methods (modified DFT methods) of calculating a DC offset component using the results of a Fourier transform and compensating for the output of a Fourier filter using the calculated DC offset component have been proposed.
These methods are advantageous in that the phasor of a fundamental frequency component can be accurately calculated, regardless of the time constant of a DC offset, but are disadvantageous in that the methods additionally require two samples to calculate a DC offset component in addition to one-cycle data required for a Fourier transform, and are vulnerable to high-frequency noise.
In order to prevent additional samples from being used in addition to one-cycle data required for a Fourier transform, a method of estimating a DC offset component using the results of a DFT of a harmonic component higher than the cutoff frequency of a low pass filter, and a method of introducing the concept of an instantaneous phasor to improve the conversion speed of a Fourier transform and eliminating the influence of a DC offset using a notch filter have been proposed. These methods can accurately eliminate the influence of a DC offset, but are greatly influenced by random noise or harmonics.
Meanwhile, a Partial Sum (PS) method of dividing one-cycle data into odd-numbered samples and even-numbered samples, performing two integral operations on the samples, and estimating a DC component using the results of the integral operations has been proposed. This method not only uses one-cycle data, but also is robust to noise. However, this method is disadvantageous in that an error is caused when the input signal contains two or more decaying DC offset components with different time constants.